1. Field of the Invention
The present invention relates to systems and methods for navigation and control of spacecraft, and in particular to a system and method for determining the inter-star-tracker misalignments of a star tracker assembly consisting of two or more star-trackers.
2. Description of the Related Art
Satellites enjoy widespread use for a variety of applications, including communications, surveillance, and data gathering. To perform their design mission, most satellites require accurate information regarding the spacecraft and payload attitude.
For applications where high bandwidth satellite attitude data is required, such data is typically obtained by on-board inertial measurement instruments such as inertial reference units having a plurality of gyros and accelerometers. However, while such instruments can provide high bandwidth information regarding the spacecraft attitude, they can only do so with respect to a attitude reference, which can be provided by a star tracker assembly (STA) having a suite of star trackers. Errors in the attitude reference propagate throughout the satellite navigation system. One source of such errors is the misalignment of the star trackers of the STA with respect to one another, and a misalignment of the STA itself with respect to the satellite body. Unless effectively nulled out or otherwise accounted for, such errors can negatively impact the satellite""s ability to carry out its service mission. What is needed is an effective method for estimating such STA misalignments and using those estimated misalignments to correct for satellite navigation errors. The present invention satisfies that need.
To address the requirements described above, the present invention discloses a method and apparatus for determining star tracker misalignments. The method comprises the steps of defining a reference frame for the star tracker assembly according to a boresight of the primary star tracker and a boresight of a second star tracker, wherein the boresight of the primary star tracker and a plane spanned by the boresight of the primary star tracker and the boresight of the second star tracker at least partially define a datum for the reference frame for the star tracker assembly; and determining the misalignment of the at least one star tracker as a rotation of the defined reference frame. In another embodiment, the method comprises the steps of measuring a position of a first star with the first star tracker; transforming the measured position of the first star in a second star tracker reference frame; measuring a position of a second star with the second star tracker; transforming the measured position of the second star in a first star sensor reference frame; identifying the first star and the second star; determining a reference position of the identified first star and the identified second star from a star catalog; computing an inner product of the measured position of the first star and the second star and the reference position of the identified first star and the identified second star, the inner product representing an error in the measured star positions. This process is repeated for a third star measured by the first star tracker and a fourth star measured by the second star tracker. The errors in the measured star positions from these measurements and transformations are equated with a measurement error equation having error parameters,       [                                                                                       ST1                            ⁢              δ                        ⁢                          xe2x80x83                        ⁢                          θ              z                                                                        δ            ⁢                          xe2x80x83                        ⁢            γ                                                                                                           ST2                            ⁢              δ                        ⁢                          xe2x80x83                        ⁢                          θ              z                                            ]    ,
wherein ST1xcex4xcex8z represents a first misalignment angular error about a boresight of the primary star tracker, xcex4xcex3 represents a second misalignment angular error as a separation angle error between the boresight of the primary star tracker and a boresight of the second star tracker, and ST2xcex4xcex8z represents the third misalignment angular error as an angular rotation angle about the boresight of the second star tracker. Using the errors in the measured positions of the first, second, third, and fourth stars, the measurement error equation for the error parameters is solved.
The present invention can also be described as an apparatus having a transformation module for transforming the position of a first star and a third star measured by the primary star tracker into a reference frame for a second star tracker and for transforming the position of a second star and a fourth star measured by a second star tracker into a reference frame for the primary star tracker; a star catalog, including reference position for each star described therein; a module for computing an inner product of a measured position of the first star and a measured position of the second star and a reference position of the first star and a reference position of the second star and a measured position of the third star and a measured position of the fourth star and a reference position of the third star and a reference position of the fourth star, the inner products representing an error in the respective measured star positions; a processor for equating the error in the measured star positions with a measurement error equation having error parameters,       [                                                                                       ST1                            ⁢              δ                        ⁢                          xe2x80x83                        ⁢                          θ              z                                                                        δ            ⁢                          xe2x80x83                        ⁢            γ                                                                                                           ST2                            ⁢              δ                        ⁢                          xe2x80x83                        ⁢                          θ              z                                            ]    ,
wherein ST1xcex4xcex8z represents a first misalignment angular error about a boresight of the primary star tracker, xcex4xcex3 represents a second misalignment angular error as a separation angle error between the boresight of the primary star tracker and a boresight of the second star tracker, and ST2xcex4xcex8z represents the third misalignment angular error as an angular rotation angle about the boresight of the second star tracker, and for solving the measurement error equation for the error parameters.